Question: Solve for $x$ : $x^2 - 11x + 24 = 0$
Explanation: The coefficient on the $x$ term is $-11$ and the constant term is $24$ , so we need to find two numbers that add up to $-11$ and multiply to $24$ The two numbers $-8$ and $-3$ satisfy both conditions: $ {-8} + {-3} = {-11} $ $ {-8} \times {-3} = {24} $ $(x {-8}) (x {-3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -8) (x -3) = 0$ $x - 8 = 0$ or $x - 3 = 0$ Thus, $x = 8$ and $x = 3$ are the solutions.